Microwave spectrum,dipole moment,and a proposed structure for 1-cyanobicyclo[1.1.0]butane

The microwave spectra of the normal and the 2-¹³C isotopic species of 1-cyanobicyclo[1.1.0]butane have been observed and assigned, leading to the following rotational constants: (normal), A=8807.202 ± 0.004, B=2924.334 ± 0.002, C=2509.322 ± 0.002 and (isotope), A=8608.85 ± 0.85, B=2902.88 ± 0.02, and C=2478.56 ± 0.02 MHz. Measurements of the second-order Stark effect led to _T=4.08 ± 0.01 D. Based on the available microwave data coupled with geometryoptimizedab initio molecular orbital structures for cyanocyclopropane and 1-cyanobicyclo[1.1.0]-butane, a molecular structure for the latter molecule is proposed. Analysis of the dipole moments of these molecules and of bicyclo[1.1.0]butane has led to the conclusion that the bicyclobutyl group is a better electron donor than is cyclopropyl. In addition, a simple frontier molecular orbital model is not sufficient for explaining all of the structural changes that occur on substituting cyano at the bridgehead of bicyclo[1.1.0]butane.     

Quantum‐chemical,IR, NMR,and X‐ray diffraction studies on 2‐(4‐chlorophenyl)‐1‐methyl‐ 1H‐benzo[d]imidazole

The title molecule, 2‐(4‐chlorophenyl)‐1‐methyl‐1H‐benzo[d]imidazole (C₁₄H₁₁ClN₂), was prepared and characterized by ¹H NMR, ¹³C NMR, IR, and single‐crystal X‐ray diffraction. The molecular geometry, vibrational frequencies, and gauge including atomic orbital (GIAO) ¹H and ¹³C NMR chemical shift values of the title compound in the ground state have been calculated by using the Hartree‐Fock (HF) and density functional theory (DFT/B3LYP) method with 6‐31G(d) basis sets, and compared with the experimental data. The calculated results show that the optimized geometries can well reproduce the crystal structural parameters, and the theoretical vibrational frequencies and GIAO ¹H and ¹³C NMR chemical shifts show good agreement with experimental values. The energetic behavior of the title compound in solvent media has been examined using B3LYP method with the 6‐31G(d) basis set by applying the Onsager and the polarizable continuum model (PCM). Besides, molecular electrostatic potential (MEP), frontier molecular orbitals (FMO) analysis, and nonlinear optical (NLO) properties of the title compound were investigated by theoretical calculations. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Perturbation calculation of atomic correlation energies for the first transition period

Results are presented for calculations of Hartree—Fock and correlation energies for the 3dⁿ 4s² and 3dⁿ⁺¹ 4s ground and excited states of the first transition series atoms using second-order Møller—Plesset perturbation theory starting with an unrestricted Hartree—Fock wavefunction.     

Ab initio calculations of relativistic and electron correlation effects in polyatomics using the universal Gaussian basis set: XeF2

Ab initio accurate all-electron relativistic molecular orbital Dirac–Fock self-consistent field calculations are reported for the linear symmetric XeF₂ molecule at various internuclear distances with our recently developed relativistic universal Gaussian basis set. The nonrelativistic limit Hartree–Fock calculations were also performed for XeF₂ at various internuclear distances. The relativistic correction to the electronic energy of XeF₂ was calculated as ～ ?215 hartrees (?5850 eV) by using the Dirac–Fock method. The dominant magnetic part of the Breit interaction correction to the nonrelativistic interelectron Coulomb repulsion was included in our calculations by both the Dirac–Fock–Breit self-consistent field and perturbation methods. The calculated Breit correction is ～6.5 hartrees (177 eV) for XeF₂. The relativistic Dirac–Fock as well as the nonrelativistic HF wave functions predict XeF₂ to be unbound, due to neglect of electron correlation effects. These effects were incorporated for XeF₂ by using various ab initio post Hartree–Fock methods. The calculated dissociation energy obtained using the MP 2(full) method with our extensive basis set of 313 primitive Gaussians that included d and f polarization functions on Xe and F is 2.77 eV, whereas the experimental dissociation energy is 2.78 eV. The calculated correlation energy is ～ ?2 hartrees (?54 eV) at the predicted internuclear distance of 1.986 Å, which is in excellent agreement with the experimental Xe—F distance of 1.979 Å in XeF₂. In summary, electron correlation effects must be included in accurate ab initio calculations since it has been shown here that their inclusion is crucial for obtaining theoretical dissociation energy (D_e) close to experimental value for XeF₂. Furthermore, relativistic effects have been shown to make an extremely significant contribution to the total energy and orbital binding energies of XeF₂. © 1995 John Wiley & Sons, Inc.     

Some properties of the bivariational Hartree–Fock scheme for complex symmetric many-particle operators

The bivariational Hartree–Fock scheme for a general many-body operator T is discussed with particular reference to the complex symmetric case: T^? = T*. It shown that, even in the case when the complex symmetric operator T is real and hence also self-adjoint, the complex symmetric Hartree–Fock scheme does not reduce to the conventional real form, unless one introduces the constraint that the N-dimensional space spanned by the Hartree–Fock functions ? should be stable under complex conjugation, so that ?* = ?α. If one omits this constraint, one gets a complex symmetric formulation of the Hartree–Fock scheme for a real N-electron Hamiltonian having the properties H = H* = H^?, in which the effective Hamiltonian H_eff (1) may have complex eigenvalues ε_k. By using the method of complex scaling, it is indicated that these complex eigenvalues—at least for certain systems—may be related to the existence of so-called physical resonance states, and a simple example is given. Full details will be given elsewhere.     

Adapted Gaussian basis sets for atoms Cs to Lr based on the generator coordinate Hartree–Fock method

We have applied a discretized version of the generator coordinate Hartree–Fock method to generate adapted Gaussian basis sets for atoms Cs (Z=55) to Lr (Z=103). Our Hartree–Fock total energy results, for all atoms studied, are better than the corresponding Hartree–Fock energy results attained with previous Gaussian basis sets. For the atoms Cs to Lr we have obtained an energy value within the accuracy of 10⁻⁴ to 10⁻³ hartree when compared with the corresponding numerical Hartree–Fock total energy results. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 858–865, 1998     

Ab initio calculations of the ground-state potential energy surface for the C?F bond decomposition in n-fluoropropane within the method for approximation of the frozen molecular fragment

The recently proposed ab initio method for calculation on many-electron molecular systems with the approximation of the inactive part of a molecule by a frozen molecular fragment was tested further in a case of the dissociation reaction of the C? F bond in n-fluoropropane. Results from the Hartree–Fock, multiple reference double-excitation configuration–interaction and second-order Møller–Plesset methods are presented. The reproduction of potential energy surfaces as well as the reproduction of electron density distribution are in excellent agreement with extended basis-set calculations. Different choices of fragments to be frozen have been examined.     

Electronic structure of UH,UF, and their ions

A relativistic effective core potential (REP) has been generated for the uranium atom and used in self-consistent-field calculations of the A states of UH, UF, and their ions. Energy curves were calculated at the base configuration level which ensures the dissociating atoms are described by Hartree–Fock wavefunctions. The electronic bonding of these molecules is found to be similar to that of comparable alkaline–earth hydrides and fluorides. The uranium 6p, 6d, and 5f orbitals retain their atomic character but the orbitals extend into the bonding region and are distorted by overlap repulsion and electrostatic effects. Nonetheless, the atomic energetic coupling determines that low energy states will have the maximum spin multiplicity and maximum orbital angular momentum projection consonant with the charge-transfer bonding.     

The perturbation theory of the extended Hartree–Fock approximation for two-electron atoms

The first-order 1/Z perturbation theory of the extended Hartree–Fock approximation for two-electron atoms is described. A number of unexpected features emerge: (a) it is proved that the orbitals must be expanded in powers of Z^?1/2, rather than in Z^?1 as expected; (b) it is shown that the restricted Hartree–Fock and correlation parts of the orbitals can be uncoupled to first order, so that second-order energies are additive; (c) the equation describing the first-order correlation orbital has an infinite number of solutions of all angular symmetries in general, rather than only one of a single symmetry as expected; (d) the first-order correlation equation is a homogeneous linear eigenvalue-type equation with a non-local potential. It involves a parameter μ and an eigenvalue ω(μ) which may be interpreted as the probability amplitude and energy of a virtual correlation state. The second-order correlation energy is 2μ²ω. Numerical solutions for the first-order correlation orbitals, obtained variationally, are presented. The approximate second-order correlation energy is nearly 90% of the exact value. The first-order 1/Z perturbation theory of the natural-orbital expansion is described, and the coupled first-order integro-differential perturbation equations are obtained. The close relationship between the first-order extended Hartree–Fock correlation orbitals and the first-order natural correlation orbitals is discussed. A comparison of the numerical results with those of Kutzelnigg confirms the similarity.     

Perturbation treatment of the Hartree–Fock equations of 1s2p3s 4Pθ state of the lithium isoelectronic sequence

The first order Hartree–Fock equations of the 1s2p3s ⁴P⁰ state of the three-electron atomic systems have been solved exactly. These solutions are used to evaluate Hartree–Fock energy up to third order with high accuracy. The third order Hartree–Fock energies for Li to Ne⁷⁺ are compared with those derived from experiment and other theoretical calculations.     

Molecular interaction energies and optimal configuration of a cubane dimer

We have studied the dependence of the binding energy of a cubane dimer on the mutual orientation of and the distance between the composing monomers employing the second‐order Møller–Plesset perturbation scheme (MP2) with the cc‐pVDZ molecular basis set. We have found that the MP2 contribution from the molecular correlations is responsible for the bound state of the cubane dimer, whereas the Hartree–Fock contribution remains anti‐bonding at all intermolecular distances. Starting with two molecules in the standard orientation and centers of mass at (0,0,0) and (0,0,d), respectively, the maximal binding energy is found at d = 5.125 Å and one of the monomers rotated by 45° about the z‐axis. This configuration implies that the hydrogen atoms belonging to different monomers tend to repel each other. The results are in agreement with experimental data on the optimal packing of cubane molecules in the solid state. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Ab initio molecular orbital study of 1-fluorosilatrane

The molecular geometry of 1-fluorosilatrane was optimized fully by restricted Hartree–Fock (HF) calculations using the 3-21G, 3-21G(d) and 6-31G(d) basis sets, with the aim of locating the positions of the local minima on the energy hypersurface. The optimized geometries were compared with available experimental (X-ray and ED) and semiempirical data. The ab initio calculations using polarized basis sets are in good agreement with those of previously reported semiempirical calculations, giving a slightly longer equilibrium Si? N distance (～ 256 pm) in the case of the endo minimum. However, the exo minimum predicted by the semiempirical methods is not supported. There was no experimental evidence for the existence of this exo minimum, and the present ab initio calculations suggest that it is highly unstable. There is considerable disagreement among the experimental results in the C? N and C? C bond lengths in various silatranes, their differences being as large as 13 pm. The present calculations predict that these differences may appear because the silatrane skeleton is flexible with low-energy, large-amplitude internal motions which introduce considerable uncertainties into the position of ring carbon atoms. © 1994 by John Wiley & Sons, Inc.     

Ab initio Hartree–Fock and configuration-interaction treatment of the interaction between two nickel atoms

The interaction between two nickel atoms in the configurations (3d)⁸(4s)² and (3d)⁹ (4s)¹ has been calculated using ab initio methods (Hartree–Fock and configuration interaction). The results of the calculations compare favorably with the optical spectrum. The discrepancy between the calculated and the experimental dissociation energy is discussed, and a new estimate of the dissociation energy is given. The configuration-interaction calculations show that the interaction between the two nickel atoms is of a very complex nature. In spite of this the binding can be interpreted in a simple way. The bond is minly due to the 4sσ_g molecular orbital while the 3d orbitals of the two nuclei are exchange coupled.     

Supplementary d and f functions in molecular wave functions at large and small internuclear separations

The CO, CO₂, CS, CIF, and SO₂ molecules were used to test the dependence of supplementary d and f function exponents to changes in bond lengths and bond angles in MO calculations utilizing Gaussian basis sets in Hartree–Fock and Moller–Plesset calculations. Using Dunning–Hay double zeta basis sets, optimizations were performed at internuclear separations from 100–200 pm and beyond. The energy cost of not reoptimizing d function exponents when bonds are stretched or compressed is much smaller for correlated calculations than for those at the Hartree–Fock level and is greatest at the lower end of the range of internuclear distances. The problem is much less serious at all levels when multiple sets of d functions are used. © 1993 John Wiley & Sons, Inc.     

Soft Coulomb hole method applied to molecules

The soft Coulomb hole method introduces a perturbation operator, defined by ?e/r₁₂ to take into account electron correlation effects, where ω represents the width of the Coulomb hole. A new parametrization for the soft Coulomb hole operator is presented with the purpose of obtaining better molecular geometries than those resulting from Hartree–Fock calculations, as well as correlation energies. The 12 parameters included in ω were determined for a reference set of 12 molecules and applied to a large set of molecules (38 homo‐ and heteronuclear diatomic molecules, and 37 small and medium‐size molecules). For these systems, the optimized geometries were compared with experimental values; correlation energies were compared with results of the MP2, B3LYP, and Gaussian 3 approach. On average, molecular geometries are better than the Hartree–Fock values, and correlation energies yield results halfway between MP2 and B3LYP. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Theoretical studies of organometallic compounds. II. All electron and pseudopotential calculations of M(CH3)nCl4 − n (M = C,Si, Ge,Sn, Pb; n = 0–4)

The performance of effective core potentials (ECP) for the main group elements of group IV has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules M(CH₃)_nCl_{4 ? n} (M = C, Si, Ge, Sn, Pb; n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G(d) and a 6-31G(d) basis set for Si, a (43321/4321/41) basis set for Ge, and a (433321/43321/431) basis set for Sn. For the ECP calculations the potentials developed by Hay and Wadt with a configuration (n)s^a(n)p^b and the valence basis set (21/21), extended by a set of d functions, are employed. © 1992 by John Wiley & Sons, Inc.     

Nonrelativistic and quasirelativistic model potential calculations on AgH and Ag2

The major relativistic effects are included into the model potential (MP) method of Bonifacic and Huzinaga. The effects are incorporated on the level of Cowan and Griffin's relativistic Hartree–Fock (RHF) method. The model potential parameters are determined using the results of nonrelativistic Hartree–Fock (NHF) and RHF calculations. A new scheme of selection of the basis functions for use in atomic and molecular MP calculations is proposed. To obtain agreement with the Hartree–Fock calculations on AgH and Ag₂, the 4p shell has to be included explicitly in the MP calculations. The explicit treatment of the 4p electrons and the resulting reduction of the core size are necessary in order to overcome difficulties with approximate representation of the large 4p–4d core-valence interactions on the MP level.